package com.fanco.learn_datastruct_leetcode.leetcode;
/**
 * 给定一个包含非负整数的 m x n 网格 grid ，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。
 * <p>
 * 说明：每次只能向下或者向右移动一步。
 * input: [[1,3,1],[1,5,1],[4,2,1]]
 * output: 7
 */
public class Day29 {
    public static void main(String[] args) {
        Solution solution = new Solution();
        int [][] grid = {{1,2,3}, {4,5,6}};
        System.out.println(solution.minPathSum(grid));
    }
    private static class Solution {
        /**
         * 动态规划：
         * 1. 状态定义
         *
         * 2. 转移方程
         *
         * 3. 初始状态
         *
         * 4. 返回值
         * @param grid
         * @return
         */
        public int minPathSum(int[][] grid) {
            if (grid.length == 0 || grid == null || grid[0].length == 0) {
                return 0;
            }
            int rows = grid.length;
            int cols = grid[0].length;
            int[][] dp = new int[rows][cols];
            dp[0][0] = grid[0][0];
            for (int i = 1; i < rows; i++) {
                dp[i][0] = dp[i - 1][0] + grid[i][0];
            }
            for (int j = 1; j < cols; j++) {
                dp[0][j] = dp[0][j - 1] + grid[0][j];
            }
            for (int i = 1; i < rows; i++) {
                for (int j = 1; j < cols; j++) {
                    dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
                }
            }
            return dp[rows - 1][cols - 1];
        }
    }
}
